Abstract
In this paper a family of methods for multi-body dynamic simulation is introduced. Equations of motion are obtained using a set of Cartesian coordinates and projected onto a set of independent relative coordinates using the concept of velocity transformation. Open-chain systems are solved directly following either a fully recursive or a semi-recursive procedure. Closed-chain systems are solved in two steps; kinematic loops are opened by removing either some kinematic joints or a rigid body, and the resulting open-chain system is solved; closure-of-the-loop conditions are imposed by means of a second velocity transformation. The dynamic formalisms have been developed so as to handle both non-stiff and stiff systems. Non-stiff systems are solved by means of an Adams–Bashforth–Moulton numerical integration scheme, which requires the computation of the function derivatives. Stiff problems are integrated by using either BDF or NDF methods, which require the computation of the residual of the equations of motion and, optionally, the evaluation of the Jacobian matrix. The proposed algorithms have been implemented using an Object-Oriented Programming approach that makes it possible to re-use the source code, keeping programs smaller, cleaner and easier to maintain. Practical examples that illustrate the performance of these implementations are included. These examples have also been solved using a commercial multi-body simulation package and comparative results are included. In most cases, the algorithms here presented outperform those implemented in the commercial package, leading to important savings in terms of total computation times.
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Rodríguez, J.I., Jiménez, J.M., Funes, F.J. et al. Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems. Multibody System Dynamics 11, 295–320 (2004). https://doi.org/10.1023/B:MUBO.0000040798.77064.bc
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DOI: https://doi.org/10.1023/B:MUBO.0000040798.77064.bc